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National and Regional Contests
Moldova Contests
EGMO TST - Moldova
2017 Moldova EGMO TST
2
2
Part of
2017 Moldova EGMO TST
Problems
(1)
Moldova tst egmo 2017
Source: MDA TST for egmo 2017, problem 2
4/26/2017
Let us denote the midpoint of
A
B
AB
A
B
with
O
O
O
. The point
C
C
C
, different from
A
A
A
and
B
B
B
is on the circle
Ω
\Omega
Ω
with center
O
O
O
and radius
O
A
OA
O
A
and the point
D
D
D
is the foot of the perpendicular from
C
C
C
to
A
B
AB
A
B
. The circle with center
C
C
C
and radius
C
D
CD
C
D
and
ω
\omega
ω
intersect at
M
M
M
,
N
N
N
. Prove that
M
N
MN
MN
cuts
C
D
CD
C
D
in two equal segments.
geometry